Particle Propagation on a Circle with a Point Interaction
arXiv:0902.0855 · doi:10.1088/1751-8113/42/27/275301
Abstract
We study a particle propagation on a circle in the presence of a point interaction. We show that the one-particle Feynman kernel can be written into the sum of reflected and transmitted trajectories which are weighted by the elements of the n-th power of the scattering matrix evaluated on a line with a point interaction. As a by-product we find three-parameter family of trace formulae as a generalization of the Poisson summation formula.
21 pages, 12 figures
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